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During several videos and documents, I have suggested “rounding pessimistically”. However, it occurred to me that folks may not understand what I mean. In this document, I’ll not only define the term, but also provide a couple of examples. Plus, at the end I’ll provide a bonus example of why this is so critical.
Let’s jump into the material.
You’ve likely heard, and probably used rounding up or down when estimating things.
The point of rounding a number is to keep it close to the original value while making it easier to use. Remember, though, when you round, you are sacrificing accuracy for convenience.
“Great”, you are saying. “I know about rounding, but you still haven’t told us what you mean by rounding pessimistically…”
OK, the online oxford dictionary defines pessimism as a tendency to see the worst aspect of things or believe that the worst will happen.
While we don’t want to be too pessimistic, assuming things aren’t going to go as expected will help make safer decisions and (hopefully) lessen the chance you have a REALLY bad day. With that in mind, we should always be rounding toward the scenario that produces the least desirable outcome.
Still confused? Let’s look at an example.
Imagine you are trying to determine how long it will take you to fly from Rochester International Airport (KRST) to St. Louis Lambert International Airport (KSTL).
The map shows a distance of 324 NM.
If your aircraft is capable of a ground speed of 124KTS, that means your trip should take 324 miles divided by 124KTS or 2.61290323 hours.
While this number is pretty accurate, it is not very friendly. So, let’s round it to something easier to use.
Since Hobbs and Tach times are usually reported in 1/10 of an hour, let’s round to the nearest 1/10th of an hour. In this case, we can either round the time down to 2.6 or up to 2.7. Which should we choose?
Let’s start by identifying which of these is the least desirable…
Is it worse to arrive earlier than expected or later than expected?
Because more time en-route means more fuel used and in my case because I’d be more likely to need to use the bathroom, the pessimistic assumption is arriving later than expected.
Therefore, for this example, rounding pessimistically would have us round up to 2.7 hours.
Now, let’s estimate how long we’ll be able to fly without stopping for fuel.
Using the same example, let’s say that weight and balance limits only allowed us to have 29 gallons of fuel in the tanks.
According to the POH, estimated fuel burn for our aircraft at 75% power is 11 gallons per hour.
Dividing available fuel by the burn rate or 29 divided by 11 gives us 2.63636364 hours worth of fuel.
Again, this number is not very friendly.
We know the airplane will run out of fuel in somewhere between 2.6 hours and 2.7 hours.
To me the least desirable outcome would be that we run out of fuel sooner. So, unlike last time, rounding pessimistically for this case would be to round down to 2.6 hours.
Now, for the bonus example, let’s put these two examples together to demonstrate why being pessimistic with these calculations is so important.
If we estimate it takes 2.7 hours to fly from KRST to KSTL and we will run out of fuel 2.6 hours after starting the engine, will we be able to make the trip without stopping somewhere for fuel?
Even ignoring the fact that regulations for daytime visual flight rules require us to have enough fuel to fly to our destination, plus an additional 30 minutes at cruise power, it seems obvious the answer is “NO”.
To avoid having to make an emergency, engine-out landing, we should stop somewhere along the way for fuel.
Could we make the trip safely if we didn’t round pessimistically?
Maybe.
Remember, the “exact” time for travel was 2.61290323 hours and we have 2.63636364 hours of fuel.
So, if everything goes perfectly there may be juuuuust enough fuel to get there. Considering the risk of being wrong, would you be willing to bet your life that things are going to work out exactly as planned?
I’m not.
There are many places where rounding can help make calculations faster or easier—determining airspeed, take off and landing performance, fuel burn, time enroute, and many more. However, we must always be aware that we are trading accuracy for convenience. And if we are not careful, we could put ourselves in a bad situation. As seen above, rounding pessimistically can make close call situations more obvious.
To summarize, rounding pessimistically means rounding toward the least desirable outcome. Remembering this rule will not only help on your next check ride, it could very well save your life and the lives of your passengers.
If you found this helpful, please share this document with anyone you think might benefit from it.
If you’d like to watch the original video, please click here: https://www.youtube.com/watch?v=7AkwJ8SLckI
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Warning: The information provided in this video is for demonstration purposes only. The information and results cannot be used for an actual flight. To plan an actual flight, you will need to use the information in the Pilot’s Operating Handbook, and the other documents associated with the specific airplane you fly.
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